For \(N\ge 1\) , Frank-Lenzmann-Silvester [1]} proved that (REF ) has a unique and non-degeneracy radial (up to translations) ground state solutions \(U(x)\in H^{s}(\mathbb {R}^{N})\) . Moreover, the ground state solution is algebraic decay
\(\frac{C_{1}}{1+|x|^{N+2s}}\le U(x)\le \frac{C_{2}}{1+|x|^{N+2s}},\) 
